Final answer:
The credit score that separates the top 20% of a normal distribution with a mean of 553 and a standard deviation of 104 is approximately 637. This score is found by using the z-score associated with the top 20% and applying it to the credit score distribution formula. Therefore, the credit score that separates the top 20% is approximately 637.
Step-by-step explanation:
To find the credit score that separates the top 20%, we will use the concept of the z-score in a normal distribution. The z-score corresponding to the top 20% can be found using a standard normal distribution table or a calculator which gives us approximately 0.84. We then apply the formula z = (X - μ) / σ, where μ is the mean, σ is the standard deviation, and X is the credit score we are trying to find.
For credit scores which are normally distributed with a mean of 553 and a standard deviation of 104, the calculation is as follows:
0.84 = (X - 553) / 104
This gives us:
X = 0.84 * 104 + 553
X ≈ 637
Therefore, the credit score that separates the top 20% is approximately 637.